JOURNAL OF APPLIED SCIENCES Electronics and Information Engineering. Cyclic MUSIC DOA TN (2012)

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1 JOURNAL OF APPLIED SCIENCES Electronics and Information Engineering Vol. 30 No. Mar. 01 DOI: /j.issn DOA 1, DOA DOA. Cyclic MUSIC.. DOA TN ) DOA Estimation of Wideband Signals Based on Cyclostationarity LIU Fu-gang 1,, DIAO Ming 1 1. College of Information and Communication Engineering, Harbin Engineering University, Harbin , China. College of Electronic and Information Engineering, Heilongjiang Institute of Science and Technology, Harbin 15007, China Abstract: For direction of arrival DOA) estimation of cyclostationarity wideband signals, by analyzing the signal s cyclostationarity and conjugate cyclostationarity properties, a new method of DOA estimation from wideband signal is proposed based on the subspace decomposition method. The new method applies signals cyclostationarity and conjugate cyclostationarity information to form an extended cyclic correlation matrix. The spatial spectrum of wideband signal is obtained. The method has good performance of the cyclic MUSIC algorithm, and does not require optimal lag time to process the wideband signals. Computer simulations are conducted to show good performance in signal selective direction finding, with high resolution and interference suppression capability. Keywords: array signal processing, DOA estimation of wideband signals, cyclostationarity, conjugate cyclostationarity 1-3]. 4] MUSIC ESPRIT Cyclic MUSIC Cyclic ESPRIT 5-7] DOA 8] MUSIC DOA 9-1] DOA No. GZ08A101) : liufugang_36@163. com diaoming@hrbeu.edu.cn

2 DOA ] DOA.. 1 M d s k t) K θ k k = 1,,, K) nt). J J. J Xf j ) = Aθ, f j )Sf j ) + Nf j ) 1) Sf j ) Nf j ) Xf j ) f j Aθ, f j ) Aθ, f j ) = aθ 1, f j ),, aθ k, f j ),, aθ K, f j )] M K aθ k, f j ) = 1, e jπfjd sin θ k)/c,, e jπfjm 1)d sin θ k)/c ] T ] T. st) m τ m m s m t) = st + τ m ) R α s ms m τ) = s m t + τ/)s mt τ/)e jπαt t t = t + τ m = st+τ m +τ/)s mt + τ m τ/)e jπαt t R α s ms m τ) = st + τ/)s mt τ/)e jπαt t e jπατm = R α ssτ)e jπατm.. α R α XXf j ) = Xf, f j + α/)x H f, f j α/) f =Aθ, f j +α/)r α SSf j )A H θ, f j α/)+r α NN f j ) +Aθ, f j +α/)r α SN f j )+R α NSf j )A H θ, f j α/) ) nt) α R α NN f j) = 0. α R α NS f j) = 0, R α SN f j) = 0 nt) nt) st). ) R α XXf j ) =Aθ, f j + α/)r α SSf j )A H θ, f j α/) 3) R α XX f j) = Xf, f j + α/)x T f, f j α/) f =Aθ, f j +α/)r α SS f j)a T θ, f j α/) 4) 3) 4) RXX α f j) RXX α f j) α. Zf, f j, α) = Xf j + α/) X f j α/) = Aθ, f j + α/)sf j + α/) + Nf j + α/) A θ, f j α/)s f j α/) + N f j α/) 5) f j α).

3 ) R α ZZf j ) = Zf, f j, α)z H f, f j, α) f 3) 4) R α ZZ f j) R α ZZf j ) = A α G α SSf j )A α ) H 6) A α = Aθ 1, α/), Aθ, α/),, Aθ K, α/), 0,, 0] 7) A α i] A α i i = 1,,, K A α i] = 1, e jπfj+ α )d sin θk)/c,, e jπfj+ α )M 1)d sin θ k)/c, 0,, 0] T i = K + 1, K +,, K A α i] = 0,, 0, 1, e jπfj α )d sin θk)/c,, ne jπfj α )M 1)d sin θk)/c ] T G α SSf j ) = RSS α f j) RSS α f j) R α SS f j)) R α SS f j)) K K M P θ, f j ) = A H θ, + α ) U N1 f j )UN1 H f j)a θ, f j + α ) A θ, f j α ) U N f j )UN1 H f j)a θ, f j + α ) R α ZZ f j) M 1 M 1). R α ZZ f j) RZZf α j ) = U S f j ) U N f j ) S 0 0 N ] V Sf j ) V N f j ) 8) U N f j ) U N f j ) = U N1f j ) U N f j ) 6) 7] U Nf j )U T Nf j ) = U N1 f j )U H N1f j ) P θ, f j ) =A α ) H U N1f j )UN1 H f j) U N1 f j )UN H f j) A α U N f j )UN1 H f j) U N f j )UN H f j) 7) 9) A H θ, f j + α )U N1 f j )UN H f j)a θ, f j α ) A θ, f j α )U N f j )UN H f j)a θ, f j α ) 10) f j P θ, f j )=arg min A H θ, f j + α ) U N1 f j )U H θ N1f j )A θ, f j + α ) A θ, f j α ) U N f j )U H N1f j )A θ, f j + α ) ] 11) 10) P θ) = 1 J J P θ, f j ) 1) j=1 Zf j, α, n) = Xf j + α/, n) X f j α/, n) 1 DFT Xf j, n) N Zf j, α, n) α

4 DOA 149 R α ZZf j ) = 1 N 3 N X m + α ) X H m α ) n=1 m RZZ α f j) R α ZZf j ) = U S f j )U N f j )] Λf j ) V Sf j ) V N f j ) 4 U N f j ) U N f j ) = U Sf j ) U N f j ) 11) f j 1). 3 3 MUSIC Cyclic MUSICWCM) f b f 0 BPSK α = kf b k = 0, ±1, ±, ) α = f 0 + kf b k = 0, ±1, ±, ). 1 BPSK f 0 = 0 MHz α = f 0. SNR 8 db 1 1 Figure 1 Target signal and interference signal arriving at the same time 1WCM DOA. WCM. MUSIC DOA.. 4 f 0 = 0 MHz BPSK 60 58, SNR 8 db. α = 10 MHz α = 1 MHz DOA Figure DOA estimation of two groups close angle signals DOA. MUSIC WCM. 1 WCM WCM. 3 BPSK f 0 = 0 MHz 0.. WCM MUSIC DOASNR 10 db 4 db 00 3.

5 RMSE Figure 3 DOA estimation RMSE of correlated signals versus SNR. 3 4 db WCM MUSIC. 4 DOA. Cyclic MUSIC.. MUSIC WCM.. : 1] Gardner W A. Cyclostationarity in communications and signal processing M]. New York: IEEE Press, 1994: ] Fusco T, Izzo L, Napolitano A, Tanda M. On the second-order cyclostationarity properties of longcode DS-SS signals J]. IEEE Transactions on Communications, 006, 5410): ]. J]. 004, 6): Chen Hui, Wang Yongliang, Pi Xingzi. The preprocessing method based on signal conjugate cyclostationary J]. Journal of Electronics & Information Technology, 004, 6): in Chinese) 4] Gardner W A. Simplification of MUSIC and ES- PRIT by exploitation of cyclostationarity J]. Proceedings IEEE, 1998, 767): ] Vvcic I P P D, Eric M. Direction of arrival estimation via exploitation of cyclostationarity, a frequency domain approach C]//Proceedings of European Conference 005, Belgrade, Serbia, 005: ] Chargé P, Wang Y D, Saillard J. A cyclostationarity exploiting direction finding algorithms J]. IEEE Transactions on Aerospace and Electronic Systems, 003, 393): ] Sahmoudi M, Amin M G. Unitary cyclic MUSIC for direction finding in GPS receivers C]//Proceedings 4th IEEE workshop on Sensor Array and Multichannel Processing, Waltham, MA, USA, 006: ] Desoki A, Takada J, Hagiwara I. Efficient array design algorithm for wide-band application of the multiple signal classification algorithm J]. Acoustical Science and Technology, 009, 303): ] Yun Huiqin, Fun H. Extended wideband cyclic music C]//IEEE Sensor Array and Multi-channel Signal Processing Workshop, 004: ] Pokrajac I P, Vucic D, Eric M. Wideband spectral cyclic MUSIC algorithm for DOA estimation C]// Proceedings of LI Conference ETRAN, Herceg Novi, 007: ] Vvcic I P P D, Eric M, Dukic M L. Cyclic MUSIC algorithm for DOA estimation of wideband coherent signals in frequency domain C]//15th Telecommunications Forum TELFOR 007: ] Gelli G, Izzo L. Cyclostationarity-based coherent methods for wideband-signal source location J]. IEEE Transactions on Signal Processing, 003, 5110): ]. J]. 009, 56): Zhang Cong, Chen Deli Lu Huanzhang. Cyclic cross-correlation based two-dimensional DOA estimation approach J]. Signal Processing, 009, 56): in Chinese) : )

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